Washington — Congress’s approval rating has never been lower, but the “broken branch” of government that Americans love to hate is progressing toward a sweeping reform of both immigration law and the federal tax code that, if they actually cross the finish line, could help unstick Washington gridlock via this simple lesson: Bipartisanship pays.

Exhibit A for the case that Congress actually works, at least on some issues? President Obama isn’t being compelled to pound the bully pulpit.

Congress’s approval rating has tanked to a historic low of 10 percent, according to a Gallup poll released Friday. Mr. Obama’s approval rating stands nearly five times that figure, at 46 percent.

Despite that approval gap, the president is lying fairly low on immigration reform and tax reform, giving key lawmakers space to try to advance legislation on two of America's most vexing and contentious issues.

The Obama administration has not “slammed the door on [tax reform], and I think at this particular stage it may be appropriate to see ‘What can the committees do? Is this real or not?’ ” said Rep. Dave Camp (R) of Michigan, the top tax reformer in the House, at a breakfast for reporters sponsored by The Christian Science Monitor on Friday.

Nodding toward his tax reform co-conspirator, Sen. Max Baucus (D) of Montana, next to him at the breakfast table, Representative Camp said, “Obviously, we’re both committed to working very hard to make this reality because we can’t afford to wait.”

During the last overhaul of the US tax code in 1986, President Ronald Reagan was out front stumping for the plan. But Obama’s lower-profile tack sits just fine with Camp and Senator Baucus, who in coming months plan a bipartisan roadshow to press the argument for tax reform beyond Washington, D.C.

Because the president has his hands off the reins, lawmakers feel they can lean in to tough policy issues with minimal political impingement. Bipartisan groups in both chambers are churning out policy options. The two tax-writing chairmen, Camp of the House Ways and Means Committee and Baucus of the Senate Finance Committee, are meeting regularly with rank-and-file members to try to ascertain where compromise might be found. Baucus, in fact, has met with all 99 other senators to talk taxes.

A long-standing split remains between Democrats, who want more tax revenue, and Republicans, who want the lowest tax rates possible. But Camp and Baucus are hoping that the work to craft better tax policy will, in the end, light the way to compromise on the overarching matter of revenues and rates.

“I’m trying to not let that stop our discussions on policy issues that would make up the tax reform bill,” said Camp. “I say, Look, let’s not go to our corners. Let’s move forward on policy and see what we get.... I don’t think it’s productive to focus on where we disagree.”

Though the White House is not publicly out front on tax reform at the moment, that doesn't mean it's disengaged, Baucus said. The senator, who has served Montana in the Senate longer than anyone else and who opted not to seek reelection in 2014 in part to pursue tax reform with all his energy, said he has met regularly with the president’s economic team and White House Chief of Staff Denis McDonough to work through tax reform questions.

But Obama has avoided inserting himself into this debate and the one on immigration so as not to scare off Republicans. “I think [Obama], wisely, is looking at tax reform the same way he’s approached immigration: carefully,” Baucus said Friday. “In this climate, it might not be wise to be too upfront too soon, because it may cause a bit of a storm.”

Republicans who are attempting to get to yes say they appreciate the president's approach.

“He’s played the right role so far. The outside cheerleader … [and] that’s been useful and effective,” said Sen. Jeff Flake (R) of Arizona, an author of the Senate’s immigration reform legislation, earlier in the week. “It would be more difficult [for Republicans in Congress] if he were out front pushing this issue.”

Make no mistake, there’s still enough partisan bickering on Capitol Hill to cause C-SPAN viewers to wince. House Republicans trotted out a full repeal of the president’s signature health-care law, bringing to at least three dozen the number of anti-Obamacare notches in their belts. Senate Democrats turned up their noses at a House GOP proposal on student loans that largely mirrors Obama’s own plan, even as the clock ticks down toward a doubling of student loan interest rates at month’s end.

Immigration reform, despite its head of steam in the Senate, faces an uncertain path through the House. And while Baucus and Camp envision pushing their tax-reform plan through during this fall's negotiation over raising the federal debt limit, the political reality is that tax code overhaul has eluded lawmakers for almost three decades.

But if Washington can break through? With a fall schedule that includes the debt ceiling, funding the federal government, and a host of other must-pass priorities, Congress will need all the confidence it can muster.

Passing an immigration bill “will be an important thing on the merits, but it will also be evidence that the institution of the United States Congress is not in fact broken and can make some hard decisions,” said Sen. Michael Bennet (D) of Colorado, a member of the Senate’s Gang of Eight who appeared with Senator Flake at a Monitor-sponsored breakfast on Wednesday. “And we are going to have to make some hard decisions on our debt and our deficit.”